Cross Sections for Charge-Exchange Reactions of the TypeH++H(n1l1m1)→H(n2l2m2)+H+

Abstract

We consider charge-exchange reactions of the general type ${\mathrm{H}}^{+}+\mathrm{H}({n}_{1}{l}_{1}{m}_{1})\ensuremath{\rightarrow}\mathrm{H}({n}_{2}{l}_{2}{m}_{2})+{\mathrm{H}}^{+}$, and use some recently derived sum rules to get comparatively simple closed expressions for the cross section. Calculations are performed in the Born approximation. We consider all excited target H atoms with ${n}_{1}\ensuremath{\ge}2$ and all (appropriate) ${l}_{1}\ensuremath{\le}3$; we average over ${m}_{1}$. We evaluate the total cross section for formation of final states with given principal quantum number ${n}_{2}$; i.e., we sum over ${l}_{2}$ and ${m}_{2}$. These results may be easily modified to include the case where the target atoms are H-like alkali atoms.